No, height is not really a consideration, sorry.
The capacity of that coop depends a whole big lot on what your climate is. If you live somewhere that is balmy and paradaisical year-round, and they're truly literally going to be out wandering around all day virtually 365 days a year, then 2 sq ft per chicken in the coop may work just fine.
If OTOH you live somewhere the weather is yucky for long stretches of time, and can't provide run space that the chickens consider sufficiently un-yucky to use all day every day, it is quite possible the chickens may spend a buncha time piled up grumpily in the coop during days/weeks of bad weather. Which can spell Trouble with a capital p-i-c-k-i-n-g.
Yes, some chickens do go out all day in the rain, in the wind, in the cold, in the snow... but, many do not. I don't know of any good way of predicting which kind yours will be, it's not just a breed thing. So IMO it is best to be careful in places with long stretches of unpleasant weather, and allow for the *possibility* that the chickens may choose to stay indoors a lot.
Good luck, have fun, welcome to BYC,
Pat